Dynamics of the higher-order-rogue-wave signals due to a coupled Noguchi electrical transmission line

We are theoretically and numerically studying the behavior of a transversely coupled Noguchi electric transmission line with a series connection of linear inductor and capacitor. Using the reductive perturbation method in the semi-discrete limit, we derive a 2D-cubic-quintic nonlinear Schrödinger equation governing the behavior of the system. Performing the generalized Darboux transformation we find higher-order rogue waves including first-, second- and third-one as solutions. Moreover, analytic predictions through Modulational Instability analysis show that the lattice can support a variety of pairs of solitons including envelope-envelope, envelope-hole, hole-envelope and hole–hole. Both rogue waves and soliton can propagate in forward or backward direction according to their frequencies. The study of the propagation properties of the rogue wave signals through the system shows that their width and velocity depend on the network parameters and wavenumbers as well as the real parameter responsible for the quintic effects. Finally, our results reveal that the network can adopt a dual right-handed or a composite right- and left-handed behavior.